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It's Stud Poker, simplified and exaggerated via regularly dealing god hands to everyone like it's going out of style.
Stud is sorta like Hold 'Em in the sense that you play with face down "hole" cards (well, card; it's just one card), however there is no communal hand. Instead, your single hole card is the difference between having a meh hand that was already exposed to the public and converting into an insane hand off the hole. Thus, as is typical of Poker, bluffing forms a core part of the game. That said, there's only so much you can bullshit in Stud, so there's a bunch of variations and rule modifications to spice the game up. In show, it is possible the dealer robot was programmed to throw out hands that greatly exaggerate their potential value in face up cards, so as to challenge players to out bluff rather than rely on known factors.